Algebraic Differential Characters of Flat Connections with Nilpotent Residues

Esnault, Hélène

doi:10.1007/978-3-642-01200-6_5

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2016

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Cited by 2 publications

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“…There are other constructions of similar functors (cf. [10]). The one we described is well-behaved with respect to R-PVHS.…”

Section: 2mentioning

confidence: 99%

Symmetric differentials and variations of Hodge structures

Brunebarbe

2016

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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Let D be a simple normal crossing divisor in a smooth complex projective variety X. We show that the existence on X-D of a non-trivial polarized complex variation of Hodge structures with integral monodromy implies that the pair (X,D) has a non-zero logarithmic symmetric differential (a section of a symmetric power of the logarithmic cotangent bundle). When the corresponding period map is generically immersive, we show more precisely that the logarithmic cotangent bundle is big.

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“…There are other constructions of similar functors (cf. [10]). The one we described is well-behaved with respect to R-PVHS.…”

Section: 2mentioning

confidence: 99%

Symmetric differentials and variations of Hodge structures

Brunebarbe

2016

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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“…After posting the preprint on the math arXiv, Deligne [De4] has indicated a construction of the Chern-Simons classes in general and Esnault has independently given a construction in [Es5].…”

Section: Introductionmentioning

confidence: 99%

A report on "Regulators of canonical extension are torsion; the smooth divisor case"

Iyer

2008

Preprint

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In this note, we report on a work jointly done with C. Simpson on a generalization of Reznikov's theorem which says that the Chern-Simons classes and in particular the Deligne Chern classes (in degrees > 1) are torsion, of a flat vector bundle on a smooth complex projective variety. We consider the case of a smooth quasi-projective variety with an irreducible smooth divisor at infinity. We define the Chern-Simons classes of the Deligne's canonical extension of a flat vector bundle with unipotent monodromy at infinity, which lift the Deligne Chern classes and prove that these classes are torsion. The details of the proof can be found in arxiv: math.AG.07070372.

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Algebraic Differential Characters of Flat Connections with Nilpotent Residues

Cited by 2 publications

References 9 publications

Symmetric differentials and variations of Hodge structures

Symmetric differentials and variations of Hodge structures

A report on "Regulators of canonical extension are torsion; the smooth divisor case"

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